Field
Embodiments disclosed herein relate generally to computed tomography (CT) imaging systems and, more particularly, to CT imaging systems configured to image the real part of the index of refraction of internal structures.
Description of the Related Art
Computed tomography (CT) systems and methods are widely used, particularly for medical imaging and diagnosis. CT systems generally create images of one or more sectional slices through a subject's body. A radiation source, such as an X-ray tube, irradiates the body from one side of the body. A collimator, generally adjacent to the X-ray source, limits the angular extent of the X-ray beam, so that radiation impinging on the body is substantially confined to a planar region defining a cross-sectional slice of the body. At least one detector (and generally many more than one detector) on the opposite side of the body receives radiation transmitted through the body in the plane of the slice, and the attenuation is measured by processing electrical signals received from the detector.
Typically the X-ray source is mounted on a gantry that revolves about a long axis of the body. The detectors are likewise mounted on the gantry, opposite the X-ray source. A single cross-sectional image of the body is obtained by taking projective attenuation measurements at a series of gantry rotation angles, and processing the resultant data using a CT reconstruction algorithm. To obtain multiple cross-sectional images or a three-dimensional image, the X-ray sources and detectors must be translated relative to the body. Either the gantry translates in a direction parallel to the long axis (i.e., perpendicular to the image plane), or the body is translated relative to the gantry. By appropriately rotating the gantry and translating the gantry or the subject, a plurality of views may be acquired, each such view comprising attenuation measurements made at a different angular and/or axial position of the source. In some CT systems, the combination of translation and rotation of the gantry relative to the body is such that the X-ray source traverses a spiral or helical trajectory with respect to the body. The multiple views are then used to reconstruct a CT image showing the internal structure of the slice or of multiple such slices.
Because X-ray CT is the most common form of CT in medicine and various other contexts, the term computed tomography alone is often used to refer to X-ray CT, although other types exist (such as positron emission tomography and single-photon emission computed tomography). Older, less preferred terms that also refer to X-ray CT are computed axial tomography (CAT scan) and computer-assisted tomography.
In one example of X-ray CT, X-ray slice data is generated using an X-ray source that rotates around the object; X-ray sensors are positioned on the opposite side of an image object from the X-ray source. Machines rotate the X-ray source and detectors around a stationary object. Following a complete rotation, the object is moved along its axis, and the next rotation started.
Newer machines permit continuous rotation with the object to be imaged slowly and smoothly slid through the X-ray ring. These are called helical or spiral CT machines. Systems with a very large number of detector rows, such that the z-axis coverage is comparable to the xy-axis coverage are often termed cone beam CT, due to the shape of the X-ray beam (strictly, the beam is pyramidal in shape, rather than conical).
A visual representation of the raw data obtained is called a sinogram, yet it is not sufficient for interpretation. Once the scan data has been acquired, the data must be processed using a form of tomographic reconstruction, which produces a series of cross-sectional images. In terms of mathematics, the raw data acquired by the scanner consists of multiple “projections” of the object being scanned. These projections are effectively the Radon transformation of the structure of the object. Reconstruction, essentially involves solving the inverse Radon transformation.
The technique of filtered back projection is one of the most established algorithmic techniques for this problem. It is conceptually simple, tunable, and deterministic. It is also computationally undemanding, with modern scanners requiring only a few milliseconds per image.
It is also possible to perform tomographic reconstruction problem using linear algebra based on matrix manipulation and matric inversion, but this approach is limited by its high computational complexity. Also, a very high number of projection measurements are required in order for the reconstruction problem not be underdetermined. More recently, manufacturers have developed iterative physical model-based maximum likelihood expectation maximization techniques. These techniques are advantageous because they use an internal model of the scanner's physical properties and of the physical laws of X-ray interactions.
Alternatively, iterative techniques provide images with improved resolution, reduced noise, and fewer artifacts, as well as the ability to greatly reduce the radiation dose in certain circumstances (e.g., reconstruct and image with only a few projections through the image object—often referred to as “few views” image reconstruction). The disadvantage of iterative techniques is they entail a very high computational requirement, but advances in computer technology and high-performance computing techniques, such as use of highly parallel GPU algorithms, now allow practical use.
One well known iterative technique is the Algebraic Reconstruction Technique (ART), also called the Kaczmarz method. This technique is essentially a method for iterative solving the matrix equation{right arrow over (g)}=M{right arrow over (ƒ)},where {right arrow over (g)} is a vector that includes all the projection measurement values, {right arrow over (ƒ)} is a vector containing the values for the estimated absorption image for the image object, and M is a matrix corresponding to the discretized Radon transform of the X-ray beams passing through the image object. By recognizing that each row vector {right arrow over (M)}i of the matrix M together with the corresponding projection value gi defines an affine space, an image of the image object can be found through successive affine projections onto the successive affine spaces corresponding to the rows of M. This iterative process converges by using the previous estimate of the image vector {right arrow over (ƒ)}m-1i to solve for the current image vector estimate {right arrow over (ƒ)}mi using the expression{right arrow over (ƒ)}mi={right arrow over (ƒ)}m-1i−{right arrow over (M)}m-1(gm-1−{right arrow over (M)}m-1·{right arrow over (ƒ)}m-1i/{right arrow over (M)}m-1·{right arrow over (M)}m-1),where each iteration progressively estimates {right arrow over (ƒ)}mi for m=2, . . . , NData, {right arrow over (ƒ)}10 is the initial guess, and the super script i indicates the ith iteration of affine projections for all values of m. The iterative process until the image estimates converge according to some predefined metric.
Typically, after each iteration through all affine projections a constraint is imposed in order to ensure convergence to a physically meaningful image. For example, in absorption imaging, the image value must be non-negative because a negative absorption value implies gain, which is not physically realistic. Therefore, the final value after each iteration, {right arrow over (ƒ)}NDatai, is subject to a predefined constraint based on a priori knowledge of the image (e.g., no gain), and the constrained final value is then used as the initial value, {right arrow over (ƒ)}1i+1, for the next iteration of affine projections. Periodically subjecting the image estimates to a predefined constraint is referred to as regularization.
Iterative reconstruction algorithms augmented with regularization can produce high-quality reconstructions for few views and even in the presence of significant noise. For few-view, limited-angle, and noisy projection scenarios, the application of regularization operators between reconstruction iterations seeks to tune the final or intermediate results to some a priori model. For example, enforcing positivity as discussed above is a simple regularization scheme. Minimizing the “total variation” (TV) in conjunction with projection on convex sets (POCS) is also a very popular regularization scheme. The TV-minimization algorithm assumes that the image is predominantly uniform over large regions with sharp transitions at the boundaries of the uniform regions. When the a priori model corresponds well to the image object, these regularized iterative reconstruction algorithms can produce impressive images even though the reconstruction problem is significantly underdetermined (e.g., few view scenarios), missing projection angles, or noisy.
The discussion of CT imaging above has been limited to absorption imaging, wherein the image is for the imaginary part of the index of refraction of the image object. Alternatively, CT imaging can be used to find an image of the real part of the index of refraction using phase contrast CT. Phase contrast CT is also known more generally as phase-contrast X-ray imaging. Phase-contrast X-ray imaging (PCI) is a general term for different technical methods that use information concerning changes in the phase of an X-ray beam that passes through an object in order to create its images. Standard X-ray imaging techniques like radiography or computed tomography (CT) rely on a decrease of the X-ray beam's intensity (attenuation) when traversing the image object, which can be measured directly with the assistance of an X-ray detector. In PCI however, the beam's phase shift caused by the image object is not measured directly, but is transformed into variations in intensity, which then can be recorded by the detector.
In addition to producing projection images, PCI, like conventional transmission, can be combined with tomographic techniques to obtain the 3D-distribution of the real part of the refractive index of the image object. When applied to image objects that consist of atoms with low atomic number Z, PCI is more sensitive to density variations in the image object than conventional transmission-based X-ray imaging. This leads to images with improved soft tissue contrast. For example, for X-rays with an energy of 23 keV, the ratio between phase shift cross section and the absorption cross section for water is 4×103. It is this large difference that is one of the motivations for performing phase contrast imaging, because phase contrast imaging has the potential to deliver contrast that is order of magnitude better than standard absorption images. Phase contrast imaging is especially beneficial for soft tissue, because soft tissues mainly consist of material of low atomic number.
Because X-ray detectors directly measure intensity rather than phase, many techniques have been developed to retrieve phase information from a series of intensity measurements. One technique simply measures the changes in the intensity profile as a function of distance from the image object. Applying diffraction theory to these in-line intensity measurements, it is possible to find the phase of the X-ray beam immediately after the image object. Propagation-based imaging (PBI) is a common name for this technique, but it is also called in-line phase-contrast CT. It consists of an in-line arrangement of an X-ray source, the image object and an X-ray detector, and no other optical elements are required. The primary difference between in-line phase-contrast CT and attenuation based CT is that the detector is not placed immediately behind the image object, but at some distance in order that the radiation beam can evolve identifiable indicia of refraction and diffraction from the image object. This simple setup and the low stability requirement provides a big advantage of this method over other methods, such as crystal interferometers and analyzer based imaging (which are not discussed here).
Under spatially coherent illumination and at an intermediate distance between image object and detector, an interference pattern with “Fresnel fringes” is created. This intermediate distance is referred to as the Fresnel regime and the Fresnel fringes results from free-space propagation for a distance greater than near-field regime, but less than the Fraunhofer Regime, at which intermediate distance the approximation of Kirchhoff's diffraction formula for the Fresnel diffraction equation is valid. In contrast to crystal interferometry the recorded interference fringes in PBI are not proportional to the phase itself, but to the second derivative (the Laplacian) of the phase of the wavefront. Therefore the method is most sensitive to abrupt changes in the decrement of the refractive index. This leads to stronger contrast outlining the surfaces and structural boundaries of the image object (edge enhancement) compared with a conventional radiogram.
Differential phase-contrast imaging is a second phase-contrast imaging method. Differential phase-contrast imaging uses Talbot interference from a series of two diffraction gratings. For this reason it is sometimes referred to as Grating-based imaging (GBI), shearing interferometry, or X-ray Talbot interferometry (XTI). The standard method for differential phase-contrast imaging consists of a phase grating and an analyzer grating.
The technique is based on the Talbot effect or “self-imaging phenomenon,” which is a Fresnel diffraction effect and leads to repetition of a periodic wavefront after a certain propagation distance, called the “Talbot length.” This periodic wavefront can be generated by spatially coherent illumination of a periodic structure, like a diffraction grating, and if so the intensity distribution of the wave field at the Talbot length resembles exactly the structure of the grating and is called a self-image. It has also been shown that intensity patterns will be created at certain fractional Talbot lengths. At half the distance the same intensity distribution appears, except for a lateral shift of half the grating period, while at certain smaller fractional Talbot distances the self-images have fractional periods and fractional sizes of the intensity maxima and minima, which become visible in the intensity distribution behind the grating, a so-called Talbot carpet. The Talbot length and the fractional lengths can be calculated by knowing the parameters of the illuminating radiation and the illuminated grating and thus gives the exact position of the intensity maxima, which needs to be measured in GBI.
In differential phase-contrast imaging, a image object is placed before the phase grating and thus the interference pattern of the Talbot effect is modified by absorption, refraction and scattering in the image object. For a phase object with a small phase gradient the X-ray beam is deflected by
  Δα  =            1      k        ⁢                  ∂                  φ          ⁡                      (            x            )                                      ∂        x            where k is the length of the wave vector of the incident radiation and the second factor on the right-hand side is the first derivative of the phase in the direction perpendicular to the propagation direction and parallel to the alignment of the grating. Since the transverse shift of the interference fringes is linearly proportional to the deviation angle of the differential phase of the wave front is measured in GBI. In other words, the angular deviations are translated into changes of locally transmitted intensity. By performing measurements with and without the image object, the change in position of the interference pattern caused by the image object can be retrieved.
Two different methods can be used to retrieve the differential phase using GBI. In the first method, phase information is separated from the other contributions to the signal using a technique called “phase-stepping.” See T. Weitkamp, et al., X-ray phase imaging with a grating interferometer, Opt. Express 13, p. 6296 (2005), incorporated herein by reference in its entirety. See also, M. Nilchaian et al., Fast iterative reconstruction of differential phase contrast X-ray tomograms, Opt. Express 21, p. 5511 (2012), incorporated herein by reference in its entirety.
In the second method, Moiré fringes are used to retrieve the differential phase. See A. Momose, et al., High-speed X-ray phase imaging and X-ray phase tomography with Talbot interferometer and white synchrotron, Opt. Express 17, p. 12540 (2009), incorporated herein by reference in its entirety. See also, N. Bevins et al., Multicontrast X-ray computed tomography imaging using Talbot-Lau interferometry without phase stepping, Med. Phys 39, p. 424 (2012)), incorporated herein by reference in its entirety.
With both of these phase-extraction methods, tomography is applicable by rotating the image object around the tomographic axis, recording a series of images with different projection angles and using back projection algorithms to reconstruct the 3-dimensional distributions of the real and imaginary parts of the refractive index.
In contrast to the differential phase contrast CT based on GBI, which requires determination of the phase in order to perform tomographic reconstruction of the index of refraction image, an exact analytic reconstruction formula has been developed for in-line phase contrast tromography by Bronnikov. See A. V. Bronnikov, Theory of quantitative phase-contrast computed tomography, JOSA A, 19, p. 472 (2002), incorporated herein by reference in its entirety. This single-step phase contrast CT processing method enables reconstruction of an image of the real part of the index of refraction directly from intensity measurements. The Bronnikov reconstruction formula is given by
            f      ⁡              (                  x          ,          y          ,          z                )              =                  1                  4          ⁢                      π            2                              ⁢                        ∫          0          π                ⁢                                  ⁢                              ⅆ                          φℱ              2                              -                1                                              ⁢                      {                                                                                                  v                    y                                                                    ⁢                                                      g                    ^                                    ⁡                                      (                                                                  v                                                  x                          ′                                                                    ,                                              v                                                  y                          ′                                                                    ,                      φ                                        )                                                                                                v                  x                  2                                +                                  v                  y                  2                                                      }                                where                    g        ^            ⁡              (                              v                          x              ′                                ,                      v            y                    ,          φ                )              =                  1        d            ⁢              ℱ        2            ⁢              {                                                            I                φ                                  z                  =                  d                                            ⁡                              (                                                      x                    ′                                    ,                                      y                    ′                                                  )                                                                    I                φ                                  z                  =                  0                                            ⁡                              (                                                      x                    ′                                    ,                                      y                    ′                                                  )                                              -          1                }            and Iφz(x′, y′) is the radiation intensity along the x′y′ plan at location z. Here, 2{•} and 2−1{•} are respectively the two-dimensional Fourier transform and the inverse two-dimensional Fourier transform. If the image object is a pure phase object, then Iφz=0(x′, y′) is independent of whether or not the image object is present. Therefore, Iφz=0(x′, y′) should already be known based on calibration measurements taken before the image was placed in the radiation path, and thus only Iφz=d(x′, y′) needs to be measured. Otherwise, if the image object is a mixed phase/absorption object both Iφz=0(x′, y′) and Iφz=d(x′, y′) need to both be measured in order to reconstruct an image of the real part of the index of refraction.
The foregoing paragraphs have been provided by way of general introduction, and are not intended to limit the scope of the following claims. The described embodiments, together with further advantages, will be best understood by reference to the following detailed description taken in conjunction with the accompanying drawings.